Methods for Measuring Tree Heights

Text for this page is extracted from the Tree Registration Manual

Prepared by Ron Flook, the former National Registrar of Notable Trees for the Royal New Zealand Institute of Horticulture.

• Indian Method
• Ruler & String (Treeby & Arthur) Method
• Vertical Angle Method

Vertical Angle Method

The equipment required is a tape measure, an instrument for taking vertical angle readings such as an Abney level or Clinometer. More up-to-date equipment is available but at a cost. Trigonometric tables for tangent and cosine and a calculator are needed. It is useful to have laminated trigonometric tables for outdoor calculations.

The height of the tree h is the sum of hl and h2
h1 is the height of the observer's eye level above ground.
h2 is the height of the tree above a point on the trunk level with the observer's eye level. h2 is found by multiplying the horizontal distance from the observer to the tree by the tangent of the vertical angle from the observer's eyes to the tree top. Note that a good reading is better taken from a distance to where the top of the tree is clearly seen. This is not always possible due to terrain but should be attempted for good results.

Example
The observer stands on level ground 36 m away from the tree being measured. The angle of 30 degrees is to the tree-top. To find h2 is the tangent of 30 degrees which is 0.577. This is multiplied by the distance from the tree 36 × 0.577 and result is 20.77 m for h2. Eye level above ground averages at 1.70 m and this is added to give the full height of the tree.

h = h2 + h1
= 20.77 m + 1.70 m
= 22.47 m

Note: To check that the ground level is constant can be done by taking a similar reading of the vertical angle to a point on the trunk to eye level.

Slopes
Should the ground slope up or down to the base of the tree one of the following formulae should be used.

Example
The height of the tree is h which is the sum of h1 and h2.

h1 is the height of eye level above ground (1.70 m).

To find h2 it is necessary to find h4. h4 is the vertical difference between tree top and eye level. This is subtracted from h3 which is the vertical difference between eye level and a point on the trunk that is the same height above ground as eye level.

h2 = h4 - h3.

To find h4 and h3 the horizontal distance from the observer to the vertical axis of the tree L2 must be found. In the example shown above the ground distance from the observer to the tree L1 is 26 m and the vertical angle from the observer to the top of h3 is 15 degrees. L2 is L1 multiplied by the cosine of 15 degrees. In this case:

L2 = L1 × cos 15 degrees
= 26 m × 0.966
= 25.12 m

To find h4:

h4 = L2 × tan 40 degrees
= 25.12 m × 0.839
= 21.08 m

To find h3:

h3 = L2 × tan 15 degrees
= 25.12 × 0.268
= 6.73 m

To find h2:

h2 = h4 - h3
= 21.08 m - 6.73 m
= 14.35 m

Therefore to find h (height of the tree):

h = h2 + h1
= 14.35 m + 1.70 m
= 16.05 m

The height of the tree h is the sum of h1 + h2 + h3.

hl is the height of eye level above ground 1.70 m (trees on sloping ground should be measured at the median of the top and bottom of the slope adjacent the trunk).

h2 and h3 are found by multiplying L2 (the horizontal distance from the observer to the vertical axis of the tree) by tangents of 15 degrees and 12 degrees respectively.

L2 is found by multiplying L1 by the cosine of 12 degrees.

Example:

To find L2:

L2 = L1 × cosine 12 degrees
= 30 m × 0.978
= 29.34 m

To find h2:

h2 = L2 × tan 15 degrees
= 29.34 m × 0.268
= 7.86 m

To find h3:

h3 = L2 × tan 12 degrees
= 29.34 m × 0.213
= 6.25 m

To find h (the height of the tree):

h = h1 + h2 + h3
= 1.70 m +7.86 m + 6.25 m
= 15.81 m